125,762 research outputs found
Diffusion of light in semitransparent media
Light diffusion is usually associated with thick, opaque media. Indeed,
multiple scattering is necessary for the onset of the diffusive regime and such
condition is generally not met in almost transparent media. Nonetheless, at
long enough times, transport in an infinite thin slab is still determined by a
multiple scattering process whose complete characterization is lacking. In this
paper we show that, after a short transient, the mean square width of the
transmitted intensity still exhibits a simple linear increase with time as
predicted by diffusion theory, even at optical thickness as low as one.
Interestingly, such linear growth is predicted not to depend neither on the
slab thickness nor on its refractive index contrast, yet the accuracy of this
simple approximation in the ballistic-to-diffusive regime hasn't been
investigated so far. By means of Monte Carlo simulations, we find clear
evidence that boundary conditions play an active role in redefining the very
asymptotic value of the diffusion coefficient by directly modifying the
statistical distributions underlying light transport in such media. In this
respect, we demonstrate the need to distinguish between a set of intrinsic and
effective transport parameters, whose relation and interplay with boundary
conditions remains to be fully understood
Hot spots and the hollowness of proton-proton interactions at high energies
We present a dynamical explanation of the hollowness effect observed in
proton-proton scattering at TeV. This phenomenon, not observed
at lower energies, consists in a depletion of the inelasticity density at zero
impact parameter of the collision. Our analysis is based on three main
ingredients: we rely gluonic hot spots inside the proton as effective degrees
of freedom for the description of the scattering process. Next we assume that
some non-trivial correlation between the transverse positions of the hot spots
inside the proton exists. Finally we build the scattering amplitude from a
multiple scattering, Glauber-like series of collisions between hot spots. In
our approach, the onset of the hollowness effect is naturally explained as due
to the diffusion or growth of the hot spots in the transverse plane with
increasing collision energy.Comment: 4 pages, 3 figure
Multiple scattering in random mechanical systems and diffusion approximation
This paper is concerned with stochastic processes that model multiple (or
iterated) scattering in classical mechanical systems of billiard type, defined
below. From a given (deterministic) system of billiard type, a random process
with transition probabilities operator P is introduced by assuming that some of
the dynamical variables are random with prescribed probability distributions.
Of particular interest are systems with weak scattering, which are associated
to parametric families of operators P_h, depending on a geometric or mechanical
parameter h, that approaches the identity as h goes to 0. It is shown that (P_h
-I)/h converges for small h to a second order elliptic differential operator L
on compactly supported functions and that the Markov chain process associated
to P_h converges to a diffusion with infinitesimal generator L. Both P_h and L
are selfadjoint (densely) defined on the space L2(H,{\eta}) of
square-integrable functions over the (lower) half-space H in R^m, where {\eta}
is a stationary measure. This measure's density is either (post-collision)
Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes
with infinitesimal generator L respectively correspond to what we call MB
diffusion and (generalized) Legendre diffusion. Concrete examples of simple
mechanical systems are given and illustrated by numerically simulating the
random processes.Comment: 34 pages, 13 figure
Dynamic characterization of cellulose nanofibrils in sheared and extended semi-dilute dispersions
New materials made through controlled assembly of dispersed cellulose
nanofibrils (CNF) has the potential to develop into biobased competitors to
some of the highest performing materials today. The performance of these new
cellulose materials depends on how easily CNF alignment can be controlled with
hydrodynamic forces, which are always in competition with a different process
driving the system towards isotropy, called rotary diffusion. In this work, we
present a flow-stop experiment using polarized optical microscopy (POM) to
study the rotary diffusion of CNF dispersions in process relevant flows and
concentrations. This is combined with small angle X-ray scattering (SAXS)
experiments to analyze the true orientation distribution function (ODF) of the
flowing fibrils. It is found that the rotary diffusion process of CNF occurs at
multiple time scales, where the fastest scale seems to be dependent on the
deformation history of the dispersion before the stop. At the same time, the
hypothesis that rotary diffusion is dependent on the initial ODF does not hold
as the same distribution can result in different diffusion time scales. The
rotary diffusion is found to be faster in flows dominated by shear compared to
pure extensional flows. Furthermore, the experimental setup can be used to
quickly characterize the dynamic properties of flowing CNF and thus aid in
determining the quality of the dispersion and its usability in material
processes.Comment: 45 pages, 13 figure
Diffusive light transport in semitransparent media
partially_open4sìIt is common knowledge that diffusion theory cannot describe light propagation in semitransparent media, i.e., media with a low optical thickness. However, even in an optically thin slab, late-time transport will be eventually determined by a multiple scattering process whose characteristics are still largely unexplored. We numerically demonstrate that, even for an optical thickness as low as 1, after a short transient, propagation along the slab plane becomes diffusive. Nonetheless, we show that such a diffusion process is governed by modified statistical distributions which result from a highly nontrivial interplay with boundary conditions.openPattelli, L; Mazzamuto, G; Wiersma, DS; Toninelli, CPattelli, L; Mazzamuto, G; Wiersma, Ds; Toninelli,
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